We say that \(\varphi \)  satisfies (aInc), if it satisfies (aInc)\(_p\)  for some \(p>1\) .
Similarly, \(\varphi \)  satisfies (aDec), if it satisfies (aDec)\(_q\)  for some \(q>1\) .
We write (Inc) if the ratio is increasing rather than just almost increasing, similarly for (Dec).
See [1]} for an interpretation of the assumptions in some special cases.
